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A100053 Maximum run of white (or OFF) cells in generation n of the Rule 30 elementary cellular automaton.

%I A100053 #21 Feb 16 2025 08:32:55
%S A100053 0,0,2,1,3,1,4,2,5,3,4,4,3,2,4,2,6,4,4,3,5,4,4,3,5,5,4,3,4,4,4,5,8,6,
%T A100053 5,3,5,4,5,3,5,5,5,9,7,5,11,9,7,6,8,6,4,7,5,3,5,6,5,4,4,5,5,3,14,12,
%U A100053 10,8,6,5,4,7,5,6,4,6,4,4,6,4,6,7,5,5,4,4,11,9,7,6,4,6,7,5,7,5,8,6,5
%N A100053 Maximum run of white (or OFF) cells in generation n of the Rule 30 elementary cellular automaton.
%H A100053 Michael De Vlieger, <a href="/A100053/b100053.txt">Table of n, a(n) for n = 0..5000</a>
%H A100053 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule30.html">Rule 30</a>
%H A100053 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%e A100053 From _Michael De Vlieger_, Oct 06 2015: (Start)
%e A100053 First 12 rows, replacing "1" with ".", ignoring "0" outside of range of 1's, for better visibility of OFF cells, maximum number of contiguous OFF cells in each row appears at left:
%e A100053 0                          .
%e A100053 0                        . . .
%e A100053 2                      . . 0 0 .
%e A100053 1                    . . 0 . . . .
%e A100053 3                  . . 0 0 . 0 0 0 .
%e A100053 1                . . 0 . . . . 0 . . .
%e A100053 4              . . 0 0 . 0 0 0 0 . 0 0 .
%e A100053 2            . . 0 . . . . 0 0 . . . . . .
%e A100053 5          . . 0 0 . 0 0 0 . . . 0 0 0 0 0 .
%e A100053 3        . . 0 . . . . 0 . . 0 0 . 0 0 0 . . .
%e A100053 4      . . 0 0 . 0 0 0 0 . 0 . . . . 0 . . 0 0 .
%e A100053 4    . . 0 . . . . 0 0 . . 0 . 0 0 0 0 . 0 . . . .
%e A100053 3  . . 0 0 . 0 0 0 . . . 0 0 . . 0 0 . . 0 . 0 0 0 .
%e A100053 (End)
%t A100053 clip[lst_] := Block[{p = Flatten@ Position[lst, 1]}, Take[lst, {Min@ p, Max@ p}]]; Max /@ Map[Length@ # &, Map[Split@ # &, Map[clip, CellularAutomaton[30, {{1}, 0}, 98]]] /. 1 -> Nothing, {2}] (* _Michael De Vlieger_, Oct 06 2015 *)
%t A100053 CellularAutomaton[30, {{1}, 0}, 100];
%t A100053 (Reverse[Internal`DeleteTrailingZeros[
%t A100053       Reverse[Internal`DeleteTrailingZeros[#]]]]) & /@ %;
%t A100053 Table[(Length /@ Select[%[[i]] // Split, Total[#] == 0 &] // Max), {i,
%t A100053     1, % // Length}] /. -\[Infinity] -> 0 (* _Philipp O. Tsvetkov_, Sep 25 2018 *)
%Y A100053 Cf. A100054, A100055.
%K A100053 nonn
%O A100053 0,3
%A A100053 _Eric W. Weisstein_, Oct 31 2004